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arXiv2013

Hermitian and non-Hermitian thermal Hamiltonians

Thermal density matrices can be described by a pure quantum state within the thermofield formalism. Here we show how to construct a class of Hamiltonians realizing a thermofield state as their ground state. These Hamiltonians are frustration-free, and can be Hermitian or non-Hermitian, allowing one to use ground-state methods to understand the thermodynamic properties of the system. In particular this approach gives an explicit mapping of thermal phase transitions into quantum phase transitions. In the non-Hermitian case, the quantum phase transition is not accompanied by a change in the spectrum of the Hamiltonian, which remains gapped. We illustrate these ideas for the classical 2D Ising model.

cond-mat.stat-mech↗
arXiv2013

Fluctuation Relations in Stochastic Thermodynamics

Fluctuation relations are identities, holding in non-equilibrium systems, that have attracted a lot of interest in the last 20 years. This is a series of 4 lectures discussing various aspects of such relations for stochastic equations modeling non-equilibrium processes.

math-ph↗
arXiv2013

Spatial evolution of tumors with successive driver mutations

We study the spatial evolutionary dynamics of solid tumors as they obtain additional driver mutations. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division occurs on the surface of the growing tumor. Each cell division has a chance to give rise to a mutation that activates an additional driver gene. The resulting clone has an enhanced growth rate, which generates a local ensemble of faster growing cells, thereby distorting the spherical shape of the tumor. We derive analytic formulas for the geometric boundary that separates the original cancer clone from the new mutant as well as the expanding frontier of the new mutant. The total number of original cancer cells converges to a constant as time goes to infinity, because this clone becomes enveloped by mutants. We derive formulas for the abundance and diversity of additional driver mutations as function of time. Our model is semi-deterministic: the spatial growth of the various cancer clones follows deterministic equations, but the arrival of a new mutant is a stochastic event.

q-bio.PE↗
arXiv2013

Electrostatic stability and encapsidation of charged nano-droplets

We investigate electrostatic stability of charged droplets, modeled as permeable, charged spheres, and their encapsidation in thin, arbitrarily charged nano-shells, immersed in a neutralizing asymmetric electrolyte background. The latter consists of a small concentration of mobile multivalent counterions in a bathing solution of monovalent (positive and negative) ions. We use extensive Monte-Carlo simulations to investigate the spatial distribution of multivalent counterions and the electrostatic component of their osmotic pressure on the bounding surface of the spherical nano-shell. The osmotic pressure can be negative (inward pressure), positive (outward pressure) or zero, depending on the system parameters such as the charge density of the droplet, the charge density of the shell, and the electrolyte screening, which thus determine the stability of the nano-container. The counter-intuitive effects of multivalent counterions comprise the increased stability of the charged droplet with larger charge density, increased stability in the case of encapsidating shell of charge density of the same sign as the charged droplet, as well as the possibility to dispense altogether with the encapsidating shell, its confining effect taken over by the multivalent counterions. These dramatic effects are in stark contrast to the conventional mean-field picture, which in particular implies that a more highly charged spherical droplet should be electrostatically less stable because of its larger (repulsive) self-energy.

cond-mat.soft↗
arXiv2013

A Scaling Theory for ac Magnetic Response in Kagome Ice

A theory for frequency-dependent magnetic susceptibility χ(ω) is developed for thermally activated magnetic monopoles in kagome ice. By mapping this system to a two-dimensional (2D) Coulomb gas and then to a sine-Gordon model, we have shown that the susceptibility has a scaling form χ(ω)/χ(0)={\cal F}(ω/ω_1), where the characteristic ω_1 is related to a charge correlation length between diffusively moving monopoles, and to the sine-Gordon principal breather. The dynamical scaling is universal among superfluid and superconducting films, and 2D XY magnets above Kosterlitz-Thouless transitions.

cond-mat.str-el↗
arXiv2013

Exact solution of a kinetic equation of one step processes of growth and decay

The exact solution of the kinetic equation of the one step process of a growth (birth) in the presence of sources (runs-off) is found for arbitrary dependence of the rate of the growth on the number of the state (or size). It is shown that the presence of the source leads on the broadening of the state (or size) distribution. It is shown also that the solution obtained can be used for approximate definition of the size distribution of nuclei for the case of large supersaturation of the vapor. The exact solution of the kinetic equation of the one step process of a decay in the presence of sources (runs-off) is found also for arbitrary dependence of the rate of the decay on the number of the state (or size).

cond-mat.stat-mech↗
arXiv2013

Correlation of the critical parameters of the gas-liquid phase transition and the density of the crystal at zero absolute temperature

The empirical formula of Timmermanns connecting the density of the crystal at zero absolute temperature with the parameters of the critical point of the gas-liquid phase transition is derived theoretically from the Van der Waals equation of state using the conditions of phase equilibrium. Two equations of state with three parameters describing the critical point of any pure substance are considered. The formula is derived approximately from the first equation and exactly from the second one.

cond-mat.stat-mech↗
arXiv2013

Note on the nature of the transition between a system in an equilibrium state and a system in a non-equilibrium state (and vice-versa)

The transition from a non-equilibrium state to an equilibrium state is characterized not only by the disappearance of the entropy production, but mainly by the disappearance of the organized currents, due to the gradients present in a non-equilibrium system. Their disappearance is necessary to obtain maximum entropy in the equilibrium state.

cond-mat.stat-mech↗
arXiv2013

Unified Jarzynski and Sagawa-Ueda relations for Maxwell's demon

By using Newtonian mechanics, we construct a general model of Maxwell's demon, a system in which the engine and the memory interact only through the exchange of information. We show that the Jarzynski relation and the two Sagawa-Ueda relations hold simultaneously, and argue that they are the unique triplet which has a natural decomposition property. The uniqueness provides a strong support to the assertion that the mutual information is the key quantity.

cond-mat.stat-mech↗
arXiv2013

Macroscopic Quantum Phenomena from the Coupling Pattern and Entanglement Structure Perspective

We explore in this paper ways to qualify and quantify the quantum entanglement $E(M)$ between two macroscopic objects by way of model studies. Knowing that a macroscopic object is a composite, how does one determine $E(M)$ in terms of the entanglements between its micro-constituents $E(μ)$? We assert that the notion of `levels of structure', the coupling strength between constituents in different levels, and the use of collective variables in each level are all pertinent factors. We consider two types of coupling, each constituent particle is coupled to only one other particle (1-to-1) versus it coupled to all particles (1-to-all). In the 1-1 case with pairwise interactions of equal strength, the entanglement is independent of the number of constituent particles $N$ in the macroscopic object. In the 1-to-all case the relative coordinates are decoupled and the center of mass (CoM) coupling scales with $N$. We provide a proof of the conditions whereby the CoM variable decouples, a cause for the special role the CoM variable plays in the entanglement between the two such macroscopic objects. This qualitative behavior is largely not affected by fluctuations in the interaction strength. We also analyzed the entanglement pattern of 4 coupled oscillators in two pairs, representing the two objects A and B (or two adjacent levels of structure), each with two constituents. By assigning different coupling strengths we can investigate the interplay of inter-level entanglement with intra- level interactions. From the entanglement dynamics of the 4-oscillator system with varying coupling strength we see the entanglement between constituents meeting sudden death while the CoM variables may sustain over longer times. This offers another way to determine under what conditions quantum entanglement between macroscopic objects can persist.

cond-mat.stat-mech↗
arXiv2013

Supercritical water: percolation transitions and a colloidal mesophase

A revised phase diagram for water shows three distinct fluid phases. There is no continuity of liquid and gas and no critical point on Gibbs density surface. A liquid state, water, spans all temperatures. A thermodynamic rigidity function, which distinguishes gas and 'liquid, shows a remarkable symmetry between complimentary corresponding states of steam and water.

cond-mat.stat-mech↗
arXiv2013

Bohm Trajectories as Approximations to Properly Fluctuating Quantum Trajectories

We explain the approximate nature of particle trajectories in Bohm's quantum mechanics. They are streamlines of a superfluid in Madelung's reformulation of the Schrödinger wave function, around which the proper particle trajectories perform their quantum mechanical fluctuations to ensure Heisenberg's uncertainty relation between position and momentum.

quant-ph↗
arXiv2013

Anomalous transport and current fluctuations in a model of diffusing Levy walkers

A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a long-tailed distribution with a finite mean but an infinite variance. Here we consider an open system with boundary injection and removal of particles, at prescribed rates, and study the steady state properties of the system. In particular, we compute density profiles, current and current fluctuations in this system. We also consider the case of a finite density of Levy walkers on the ring geometry. Here we introduce a size dependent cut-off in the time of flight distribution and consider properties of current fluctuations.

cond-mat.stat-mech↗
arXiv2013

Numerical approach to unbiased and driven generalized elastic model

From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM), that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces. We compare analytical and numerical results for the subdiffusion exponent beta characterizing the growth of the mean squared displacement <(delta h)^2> of the field h described by the GEM dynamic equation. We study the scaling properties of the qth order moments <|delta h|^q> with time, finding that the interface fluctuations show no intermittent behavior. We also investigate the ergodic properties of the process h in terms of the ergodicity breaking parameter and the distribution of the time averaged mean squared displacement. Finally, we study numerically the driven GEM with a constant, localized perturbation and extract the characteristics of the average drift for a tagged probe.

cond-mat.stat-mech↗
arXiv2013

Statistical Mechanics of Multistability in Microscopic Shells

Unlike macroscopic multistable mechanical systems such as snap bracelets or elastic shells that must be physically manipulated into various conformations, microscopic systems can undergo spontaneous conformation switching between multistable states due to thermal fluctuations. Here we investigate the statistical mechanics of shape transitions in small elastic elliptical plates and shells driven by noise. By assuming that the effects of edges are small, which we justify exactly for plates and shells with a lenticular section, we decompose the shapes into a few geometric modes whose dynamics are easy to follow. We use Monte Carlo simulations to characterize the shape transitions between conformation minima as a function of noise strength, and corroborate our results using a Fokker-Planck formalism to study the stationary distribution and the mean first passage time problem. Our results are applicable to objects such as such as graphene flakes or protein β-sheets, where fluctuations, geometry and finite size effects are important.

cond-mat.stat-mech↗
arXiv2013

Modeling the interaction of an arbitrary light field with a diffraction grating by the Monte Carlo method

A high-accuracy solution of the diffraction problem has become necessary for the treatment of certain special questions of statistical physics. This article reports the creation of a computer program that serves as an instrumental method of calculating the parameters of diffraction phenomena when complex optical systems are being theoretically investigated. The program solves the diffraction problem by a rigorous method based on Maxwell"s equations under specified boundary conditions. An arbitrary for instance, diffuse configuration of the initial light field is allowed. Reflective gratings with a linear or crossed sinusoidal profile of the surface micro relief are considered as the diffraction optical elements. The characteristics of the self-consistent total light field can be calculated when several diffraction elements are present in the system.

physics.optics↗
arXiv2013

Spectral community detection in sparse networks

Spectral methods based on the eigenvectors of matrices are widely used in the analysis of network data, particularly for community detection and graph partitioning. Standard methods based on the adjacency matrix and related matrices, however, break down for very sparse networks, which includes many networks of practical interest. As a solution to this problem it has been recently proposed that we focus instead on the spectrum of the non-backtracking matrix, an alternative matrix representation of a network that shows better behavior in the sparse limit. Inspired by this suggestion, we here make use of a relaxation method to derive a spectral community detection algorithm that works well even in the sparse regime where other methods break down. Interestingly, however, the matrix at the heart of the method, it turns out, is not exactly the non-backtracking matrix, but a variant of it with a somewhat different definition. We study the behavior of this variant matrix for both artificial and real-world networks and find it to have desirable properties, especially in the common case of networks with broad degree distributions, for which it appears to have a better behaved spectrum and eigenvectors than the original non-backtracking matrix.

physics.soc-ph↗